## Casting out 9s

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### Casting out 9s

I want to prove whether or not 65,547,012/26,436 = 2479 + (12,168/26,436) using casting out of 9s.

I know how casting out 9s works with multiplication. However, I do not know how to apply the concept to division with a remainder/decimals. Please help me get started. Thanks!
SlamDunk
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### Re: Casting out 9s

The dividend excess is 3. The final excess from the remaining values is $$$3\times 4$$+0=3$. The values check.
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
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### Re: Casting out 9s

Ok I see that the dividend is 6+5+5+4+7+0+1+2 has a remainder of 3 when divided by 9. I also see that 2+6+4+3+6 has a remainder of 3 and that 2+4+7+9 has a remainder of 4 and that you multiply both of those.

The fraction is what is getting me. How do you know it has remainder of 0?
SlamDunk
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### Re: Casting out 9s

12,168 is divisible by 9 and 26,436 is divisible by 3 but not 9, so you can at least conclude that the quotient is divisible by 3.
Pari/GP: this is the program I probably mentioned in my post. Windows users can get it at http://pari.math.u-bordeaux.fr/pub/pari ... -2-6-1.exe

CRGreathouse
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### Re: Casting out 9s

65,547,012 = 2479·26,436 + 12,168

then use the method:

3 = 4·3 + 0 = 3
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
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### Re: Casting out 9s

Thanks Mark. That is very clever and makes perfect sense.
SlamDunk
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### Re: Casting out 9s

I will be honest and admit I had never heard of this method before and had to look it up.
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
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